In general, polygonal products, such as bolt heads, are manufactured by using, for example, a milling machine. In this case, the peripheral surface of a polygonal portion, including a plurality of faces, must be formed face by face, thus entailing a long working time and high working cost. As a measures for eliminating such an awkward situation, polygon working is known. In this method, a workpiece is worked to form a portion having a polygonal section using one or more cutters of a tool by relatively feeding the workpiece mounted on one main spindle of a machine tool and the tool mounted on the other main spindle, while rotating the workpiece and the tool with a predetermined rotational speed ratio (International Application No. PCT/JP87/00795).
According to the polygon working, a workpiece can be quickly worked to have a square or hexagonal form at low cost by rotating, for example, a tool having two cutters arranged at an angular distance of 180.degree. from eath other in the circumferential direction of the tool, or a tool having three cutters arranged at intervals of 120.degree. in the circumferential direction of the tool at a speed twice as high as the rotational speed of the workpiece, using a relatively low-priced lathe.
However, in forming a polygonal portion on the workpiece that a specific region of the polygonal portion, e.g., an angle of the polygonal portion, is in alignment with a predetermined circumferential position on the workpiece, even where the respective rotations of the workpiece and the tool are simultaneously started with the cutter(s) of the tool situated in the predetermined circumferential position on the workpiece, and the relative feed of the workpiece and the tool is started when a steady-state operation mode is established for enabling the workpiece and the tool to rotate with a predetermined rotational speed ratio, it is actually difficult to align the angle of the polygonal structure accurately with the predetermined circumferential position on the workpiece. Thus, it is difficult to manufacture a product such that, for example, an angle of a hexagonal portion formed on one end of the product and its corresponding angle of a square portion formed on the other end of the product are accurately in alignment with each other with respect to the circumferential direction of the workpiece.